Examples of these measurement instruments include: platform navigation systems, sensors for scene detection and analysis and, in certain instances, weapons to deter or assail targets in security or combat missions.                The navigation system traditionally uses, for its positioning, an inertial rig comprising gyrometers, accelerometers and processing operations for the platform attitude calculation; a GPS as well as a barometer also contribute to its positioning and their measurements are fused with the inertial measurements, for better quality of the general navigation solution.        Systems for scene detection and analysis comprise optronic sensors with detectors operating from the visible region to the infrared for acquiring a video of the scene, a telemeter for measuring the distance thereto. The line of sight (or LoS) of the sensor has an ability to orient itself with agility so as to rapidly acquire a zone of the scene corresponding to the instantaneous field of vision of the sensor. Inertial measurement units or other opto-mechanical devices are further used to measure the attitude of the LoS with respect to a reference of the sensor or in an absolute manner.        Weapons systems comprise inertial and positioning means for guiding munitions toward their objectives. They may moreover use homing heads based on optronic imaging or radar to correct their terminal guidance onto the designated targets.        
In the conventional calibration procedures, the instruments or equipment need to be aligned with the reference system of the platform and their respective positionings need to be “harmonized”.
This optronic system is generally installed on a platform aboard an aircraft or more generally aboard a vehicle whose known position is for example provided by an inertial rig.
The determination of the defects of mounting of the system on the platform and of the defects of the measurements performed by the instrument is a step prior to any location or pointing procedure, in particular when the latter involves measurement instruments distributed over the system.
Mounting defects are manifested by a non-alignment of the reference axes of the coordinate frame of the platform with those of the coordinate frame of the measurement instrument. The operation of measuring the angles representing the transformation between coordinate frames is a procedure dubbed harmonization, when it entails mutually orienting the measurement instruments; or alignment when it entails orienting (or positioning) them in relation to the reference coordinate frame of the system (boresight alignment).
In addition to the errors of orientation related to the reference axes of the measurements of angles (in particular demarcated by the axes of gyrometers in inertial systems), the mounting of a sensor on a platform of airborne type introduces deviations of orientation between the reference axes of the platform and of the sensor of possibly as much as several degrees. A commonplace value of the errors in the knowledge of the mounting angles is of the order of 10 mrad.
These errors originate from the production of various hardware components such as the quartz, which regulates clocks, the accelerometers, which measure accelerations, and demarcate the directions of axes around which gyrometers measure angular speeds.
The attitude of the system is typically marred by an error of about 1 mrad when the information arises from an inertial rig of aeronautical class.
Instruments for measuring angles and/or distances commonly introduce a bias of a few milli-radians.
During operation, the platform and the reference axes may undergo mechanical and thermal deformations in particular caused respectively by a strong acceleration or deceleration and by the variation in the flying height. These thermomechanical constraints induce, on the measurements, a bias of possibly as much as a few mrad.
Among measurement defects may be cited, notably, noise, biases, scale factors and drifts. The scale factor is manifested by a deviation of the magnitude measured with respect to the true value whose value is proportional to the value of the magnitude. Its order of magnitude is a few tens of parts per million (ppm for short). The drift is manifested by a deviation in the magnitude, which grows over time from a date at which the latter was corrected. One speaks of slow drift if the increase is small in relation to the value. When the time span of the measurements is small enough for the deviation in drift not to be important, it may be processed as an extra bias over the time interval considered.
For the measurements of angles the specific mounting values may be of the order of about ten degrees whereas the aggregate of the defects leads to residual errors of about 10 mrad. The translations between the coordinate frames of the platform represent deviations of possibly as much as a few meters with residual errors, which are controlled so as to be a few centimeters.
The parameters that we propose to estimate relate equally well to the defect of a measurement of an apparatus pertaining to on-line information as to the mounting of the equipment on the platform.
There exist several calibration schemes with variations inherent to the field of application.
In the field of metrology, measurement is necessary for any knowledge, for any decision taking and for any action. Characterization of the defects of measurement instruments constitutes a systematic step within the production of elementary instruments or sensors integrated within complex systems or sensors. This characterization is manifested in a conventional manner by the estimation of properties (bias, scale factor, etc.) of the physical magnitudes (angle, distance, etc.), characterized by their statistical values (mean, standard deviation, etc.) over the field of use of the system.
The metrology operations are generally performed on the ground on test beds and in a very precise manner but under particular measurement conditions which cannot always reflect the real conditions of use. These calibration procedures are expensive, laborious, and difficult to carry out through lack of room within the equipment; moreover the realization on the ground of the conditions of acquisition (distance, temperature, mechanical constraint) and of modeling remains limited by the knowledge of the phenomena.
To determine the ground alignment, the metrology operations are lengthy and consume specific means. They have moreover to be potentially repeated, thus rendering them very expensive and unsuited to fast and practical use of the instruments on mobile platforms.
Moreover, measurement instruments are subject to phenomena of temporal drift and aging that may modify their bias. This assumes a strategy of maintaining operational condition (MCO), with plans regarding resumption of testing and calibration.
In the field of industry, and for robotic applications, means are commonly implemented to carry out the calibration of pose (position and orientation) of mechanical items or parts relating to a fixed or mobile structure as described in the article by P. Renaud and co-authors “Optimal pose selection for vision-based kinematic calibration of parallel mechanisms”, Proceedings of the 2003 IEE/RSJ. Conference on Intelligent Robots and Systems. Las Vegas. Nev. October 2003.
These operations traditionally consist in estimating the position and the orientation of the mechanical part or item in relation to a fixed or mobile structure on the basis of a model.
The measured information is of high precision but often relative. For our application, a scheme making it possible to directly evaluate the global orientation is sufficient and absolute information is sought.
Moreover the calibration of the systems with which we are concerned often exhibit a significant number of joints or gimbals (see for example FIGS. 10, 15, 16, 17 in “Air Reconnaissance Primary Imagery Data Standard” Edition 4 of 14 Mar. 2006).
In the medical setting, in conjunction with robotics and enhanced reality, means are being developed for assisting tricky operations requiring accuracy of positioning in surgical interventions, as described for example in T. Sielhorst T and co-authors “Advanced Medical Displays—A Literature Review of Augmented Reality”, J. of Display technology, Vol 4 No 4 Dec. 2008
The solutions afforded in respect of the medical field cannot be produced in a dynamic and non-cooperating setting. In these applications, knowledge of the setting makes it possible for example to prearrange markers or to learn certain characteristics of the environment so as to position and orient the equipment used. Moreover the information produced is often relative, whereas for the location or pointing application, absolute information is sought.
In medicine, as for the other applications mentioned, the processes are not autonomous since they are based on reference data (considered to be exact) on the environment, or on exchanges of information in the form of cooperation between distributed systems or on a specific intervention of the user.
To position an object by triangulation in the presence of bias, certain authors such as Mangel in “Three bearing method for passive triangulation in systems with unknown deterministic biases”, IEEE TAES Vol 7 No 6 Nov. 1981, have favored schemes able to provide a solution which is not too disturbed by their presence. But these approaches do not afford finer knowledge of the system so that it can be better utilized under new conditions.
In the field of positioning and navigation, fairly recent works seek to correct measurement defects by using physical redundancies (duplication of the measurement instruments) or software. These approaches relate essentially to GPS positioning and orientation systems (INS), such as described by Pittelkau in “Calibration and Attitude Determination with Redundant Inertial Measurement Units”, J. of Guidance Control and Dynamics. Vol. 28, No. 4, July-August 2005.
But the use of physical redundancies exhibits recurrent costs and makes it necessary to borrow existing architectures. Problems regarding bulkiness and room available within the equipment must also be taken into account. Finally they do not make it possible to measure the alignments on all the useful gimbals for the system.
In the military field, the fusion of data entails specific needs and in particular with the need for associating diverse data:                For multi-sensor tracking, academic works have been concerned with the training of surveillance radar antennas on Geographic North so as to improve the tracking of aircraft by several radars on the scale of a country or even a continent. Within this framework may be cited the work carried out by:                    Li and co-authors “A real-time bias registration algorithm for multiradar systems”, 7th International Conference on Signal Processing (IEEE) 2004, or else,            Dong and co-authors “A generalized least squares registration algorithm with Earth-centered Earth-fixed (ECEF) coordinate system”, 3d International Conference on Computational Electromagnetics and Its Applications Proceedings 2004,                        For location in the presence of angular bias, the calibration (or boresighting) operation consists in carrying out an adjustment which makes it possible to align the Line of Sight (or “LoS”) on the sighting axis of the optronic system installed on a platform.        For the exchange of information between distributed sensors, the necessity for interoperability favors the development of normalization, in the realms of positioning and of fusion between heterogeneous sources. STANAG 5516, the acronym standing for the expression “STANdard AGreement”, reserves specific fields (designated by PPLI for Precise Participant Location and Identification) to allow the exchange of the known positions between the participants of the network for cooperative calibration.        
For applications using cooperating measurement instruments, data fusion offers advantages in terms of autonomy and independence to the environment. On the other hand, they pose constraints relating to the number and distribution of measurement instruments and require means of communication and information exchange to these instruments, as well as an identification of common objects to which the information to be reconciled pertains. This situation does not correspond to the desired use.
Airborne measurement instruments evolve under fairly different thermomechanical conditions from what may generally be reproduced on the ground under realistic conditions with all the diversity encountered in their area of operation.
Whatever the area of application, these locating instruments require systematic and periodic checking in order to manage their temporal drift and their aging.
Calibration procedures are expensive, laborious, and difficult to carry out through lack of room within the equipment; it is also difficult to realize on the ground the conditions of acquisition (distance, temperature, mechanical constraint) and of realistic modeling which remains limited by the knowledge of the phenomena.